Answer:
m - n = 501
Step-by-step explanation:
Remark
The first thing you have to do is find the number of odd and even numbers. This is where you have to be careful because there is a danger of being out by one.
equation
l = a + (n - 1)*d
Solution even
l = 1000
a = 2
d = 2
1000 = 2 + (n - 1)*2
998/2 = (n - 1) * 2 / 2
499 = n - 1
n = 500
Solution odd
l = 1001
a = 1
d = 2
1001 = 1 + (n - 1)*2
1000 = (n - 1)*2
1000/2 = (n - 1)2/2
500 = n - 1
501 = n
Sum Even of even numbers from 1 to 1001
Givens
a = 2
n = 500
l = 1000
Equation
Sum = (a + l ) * n / 2
Solution
Sum = (2 + 1000)*500/2
Sum = 1002 * 250
Sum = 250500
Sum of Odd numbers from 1 to 1001
a = 1
l = 1001
n = 501
Equation
sum = (a + l)*n/2
sum = (1 + 1001) * 501
sum = (1002)*501 / 2
Sum = 251001
Answer
m - n = 251001 - 250500 = 501
Step-by-step explanation:
Since it's a direct variation
y = kx
where k is the constant of proportionality
To find the value of y when x = –0.5 we must first find the relationship between the variables
When
x = 3
y = 2
2 = 3k
Divide both sides by 3
So the formula for the variation is
<h3>
</h3>
When x = - 0.5 or - 1/2
We have the final answer as
<h2>
</h2>
Hope this helps you
X is the radius of the slice. So we must find the equation of the side of the cone.
y=mx+b, so now we must use two points to solve for the slope, or "m".
m=(y2-y1)/(x2-x1)
m=(0-15)/(5-0)
m=-15/5
m=-3 so our line so far is:
y=-3x+b, b=y-intercept=value of y when x=0, which we can see is 15 ft so:
y=-3x+15
Now the radius is x, so we must solve for x from the equation above...
-3x+15=y subtract 15 from both sides
-3x=y-15 divide both sides by -3
x=(15-y)/3
And area of this circle is:
A=πx^2, and using x found above:
A=(π/9)(15-y)^2
A=(π/9)(225-30y+y^2), so when y=6 ft
A=(π/9)(225-30*6+6^2)
A=(π/9)(81)
A=9π or if we let π=pi
A=9pi ft^2
Answer:
33.49 cubic inches
Step-by-step explanation:
Answer:
Step-by-step explanation:
we know that
The surface area of a rectangular prism is equal to
where
B is the area of the base
P is the perimeter of the base
h is the height
In this problem we have
substitute
